What a difference a queen makes. It was the royal visits by Anne in the opening years of the 18th century that turned this sublimely placed town from relative backwater to fashionable Georgian gem and set in train its graduation to Unesco world heritage site. Look at the plentiful shopfronts on a bright, reflective day and you are staring the local industry in the face. It is you, curious visitor. Take heart; there are elegant, honey-stoned reasons for the place being such a centre of tourism and they declare themselves the moment you start this 2½-mile walk from the Bath Spa railway station.

Immediately left into Dorchester Street, and on the right is a colonnaded three-storey building that in another life might have been a seat of regional government. But as we are in Bath, it is a Debenhams. This kinship of commerce and comeliness runs through the town like the lettering in a stick of rock – or it would do if Bath was in to sticks of rock, which it’s not. A right turn up St Lawrence Street takes you into Southgate and the first of the town’s two main car-free zones; this precinct is about one half of the land that used to be known as The Ham. Bath may not be as militantly pedestrianised as York but these enclaves are an appropriate blessing for such a compact centre. Deep beneath these pavements lies the guiltless secret of nearly one thousand parking spaces.

Out of Southgate at its north-west quarter, continue up St Lawrence Street, across the junction into the once literally titled street of Lower Borough Walls. First for the Romans, who called the town Aquae Sulis, then for the fortified burgh of the Anglo-Saxons, the now almost-vanished fortifications made the place a formidable redoubt against offcomers – in fact, the very opposite of its welcoming present self.

Carry on up Westgate Buildings, over Westgate Street, with the popular Komedia club on the corner, and into Saw Close, home of the Theatre Royal; two centuries old and once host to such players as William Macready and Edmund Kean. North again up Barton Street to the south-east corner of Queen Square, welcome for its sudden green spaciousness. Up Gay Street to number 40, on the right, just above Old King Street. Here is the Jane Austen Centre, a few doors down from one of the houses in which the author lived during her time in Bath, between 1801 and 1806.

Austen powers … a shop window with a display of Bath gin and a portrait of Jane Austen, who lived in city from 1801 to 1806

Two of her six novels – Northanger Abbey and Persuasion – are set in the town. In the course of their narration Bath changes from being a backdrop to a virtual character, full of airs that are not of the healthiest kind. What for Catherine in the first book was elevating has become, for Anne in the second, enervating. Perhaps, given the hot springs that gave the city its name, the best word is immersive. Austen’s biographer Claire Tomalin reckons you can almost sense her rolling her eyes at the charade of its high society. All this is relevant – as we are bound for some of the places, such as the Assembly Rooms, Baths and Pump Room, that informed her vision.

First, go left from Gay Street into Queens Parade Place, which brings you to the southern tip of Royal Victoria Park. When you turn right into the imposing Royal Avenue, you also happen to be treading one of the country’s best long-distance footpaths, the Cotswold Way, which goes from the steps of Bath Abbey to Chipping Campden in Gloucestershire, 100 miles away. For today, be content with turning right at the park’s western exit and walking up Marlborough Road to Royal Crescent.

If Bath is a style statement to the rest of the nation, then this mighty confection, the ultimate croissant overlooking the capital of tea shops, stands in a similar relation to Bath. It cannot help but show off, feature in films and be, rightly or wrongly, a defining image for a vastly more varied entity. It has been lived in by all manner of people since its design by John Wood the Younger in the 1760s, from the anti-slavery MP William Wilberforce to Isaac Pitman, whose name is shorthand for shorthand.

Its neighbour to the east along Brock Street is no slouch. This is the equally magnificent Circus, a sort of residential Colosseum. It gets its validation not by preening outwards but by viewing itself whenever it looks out of the window. You can barely move for friezes, serpents and symbols on the classic facades, with the three orders of Doric, Roman and Corinthian placed in ascending order like the layers of a doughnut-shaped cake.

This one is the work of John Wood the Elder who apparently intended the configuration of Circus, Gay Street and Queen Square to form a masonic key-shape when viewed from above. Thanks to 21st-century mapping, we can now do just that, and there it plainly is, a big old, churchwarden-type key lodged in the streetscape.

Off from The Circus at an angle of two o’clock and you come to Bennett Street and The Assembly Rooms, another Wood the Younger design. Robert Adam wanted the contract but his proposals were too expensive. Wood raised the money through an 18th-century version of crowdfunding known as a Tontine. The reason for this societal hub being sited so far from the centre was that the growing popularity of the waters had boosted tourist and residential interest in the town and speculative building was pushing its way north.

Use the clutch of walkers-only streets – Saville Row immediately to the east of the Rooms, then over Alfred Street into Bartlett Street, right into Andrew’s Terrace, which rightangles leftwards into Miles’ Buildings. Left into the relative bustle of George Street, first right down Milsom Street next left at Green Street, bearing to the right by the Postal Museum, into Northgate Street. And so to Bridge Street, with the Victoria Art Gallery on the right just before you reach the bridge in question.

Making a ponte … Pulteney Bridge and the Grand Parade on the river Avon. The bridge’s design was inspired by Florence’s Ponte Vecchio Photograph: Alamy

Not just any old bridge but the remarkable Pulteney Bridge which, if you are using it to cross the Avon, passes itself off as a shop-lined street, albeit shops with sudden and spectacular views over the water from their rear windows. It was inspired by the Ponte Vecchio in Florence. Down Grand Parade, right into Orange Grove and arrive at the great Abbey, the third building on this site, famous for its ladder of angels in the west front, allegedly the response to the visionary dream of the Bishop of Bath, Oliver King in the late 15th century. The monastery that once stood here was the location, in 973, of the crowning of Edgar, perhaps the first king to unite England.

Just a few yards away are the Roman Baths, an appropriate destination for a secular pilgrimage. For it is here that the city got not only its name but also its endless and unique (in Britain) supply of hot water. This fell as rain some 10 millennia ago and sank to a mile and a half below ground. Heated by rocks, up it comes again at a temperature of 45C, before cooling to 34C.

You can swim in it if you want, or rather, take the waters. Not at the old Roman Baths themselves, which are for viewing only, but in a purpose-built centre with a high roof pool on Hot Bath Street. Here you can loll among the shapes of the town’s famous masonry and catch sight of the surroundings hills. That’s when I learned something new. The hills ring the place. There’s even – for another day – a circular walk, looking down on all this ornamentation. We’re in a gigantic dip in the Earth. Bath, so cool in many ways, has something volcanic about it.

From Hot Bath Street, head back to the station via Beau Street, Stall Street and Henry Street. This brings you to Manvers Street, into which you turn right and can make out the railway station two hundred yards away. Built in 1840 by the great Brunel, it’s a Grade II-listed building in an asymmetrical Tudor style with curving gables. Did you expect anything less?